Friday, August 11

My program for finding pandigital factorization integer cascades wasn't very efficient. In order to improve on that situation I decided to first calculate a table of possible end-PFIs resulting from the addition of pandigital numbers to all possible start-PFIs. By which I mean the smallest few hundred-thousand start-PFIs because — after that — there are unlikely to be additional solutions:

The graph shows the number of solutions for the smallest 431285 PFIs. I went this far because there is a solution at PFI #431284 (which, after the addition of a pandigital number, becomes PFI #431285). The largest number of solutions is 414 for PFI #39644, which is 554556098 or 2*5861*47309:

Next I calculated a table of all possible PFIs that result from the subtraction of pandigital numbers from a given PFI:

This graph shows (again) the number of solutions for the smallest 431285 PFIs. The largest number of solutions is 575 for PFI #301365, which is 8283333125 or 5^4*1609*8237:

1. 5^4*1609*8237 - 8197423605 = 2^4*5*1073869

2. 5^4*1609*8237 - 8137426590 = 5*2789*10463

3. 5^4*1609*8237 - 8136720459 = 2*4637*15809

4. 5^4*1609*8237 - 8127509346 = 59*107*24683

5. 5^4*1609*8237 - 8124903765 = 2^4*5*1980367

6. 5^4*1609*8237 - 8109472635 = 2*5*17386049

7. 5^4*1609*8237 - 8109264735 = 2*5*17406839

8. 5^4*1609*8237 - 8104723695 = 2*5*17860943

9. 5^4*1609*8237 - 8103724695 = 2*5*17960843

10. 5^4*1609*8237 - 8103624759 = 2*167*538049

11. 5^4*1609*8237 - 8096254731 = 2*173*540689

12. 5^4*1609*8237 - 8057142936 = 83*107*25469

13. 5^4*1609*8237 - 8051964723 = 2*17*6804953

14. 5^4*1609*8237 - 8026579431 = 2*83*1546709

15. 5^4*1609*8237 - 8025471639 = 2*149*865307

16. 5^4*1609*8237 - 7980651324 = 283*1069547

17. 5^4*1609*8237 - 7962401358 = 13*24687059

18. 5^4*1609*8237 - 7946052183 = 2*197*856043

19. 5^4*1609*8237 - 7942506183 = 2*197*865043

20. 5^4*1609*8237 - 7934502186 = 17*2543*8069

21. 5^4*1609*8237 - 7920348156 = 17*53*402869

22. 5^4*1609*8237 - 7916084532 = 14639*25087

23. 5^4*1609*8237 - 7908426315 = 2*5*37490681

24. 5^4*1609*8237 - 7902861435 = 2*5*38047169

25. 5^4*1609*8237 - 7901628435 = 2*5*38170469

26. 5^4*1609*8237 - 7895130462 = 149*2605387

27. 5^4*1609*8237 - 7865043219 = 2*5417*38609

28. 5^4*1609*8237 - 7861930524 = 157*2684093

29. 5^4*1609*8237 - 7854312096 = 47*89*102563

30. 5^4*1609*8237 - 7845629310 = 5*29*3018647

31. 5^4*1609*8237 - 7829051364 = 2903*156487

32. 5^4*1609*8237 - 7821946035 = 2*5*46138709

33. 5^4*1609*8237 - 7819462035 = 2*5*46387109

34. 5^4*1609*8237 - 7815649320 = 5*1487*62903

35. 5^4*1609*8237 - 7813256940 = 5*23*4087619

36. 5^4*1609*8237 - 7809642315 = 2*5*47369081

37. 5^4*1609*8237 - 7804316295 = 2*5*47901683

38. 5^4*1609*8237 - 7804269315 = 2*5*47906381

39. 5^4*1609*8237 - 7802963415 = 2*5*48036971

40. 5^4*1609*8237 - 7802693415 = 2*5*48063971

41. 5^4*1609*8237 - 7802619435 = 2*5*48071369

42. 5^4*1609*8237 - 7802613495 = 2*5*48071963

43. 5^4*1609*8237 - 7802396415 = 2*5*48093671

44. 5^4*1609*8237 - 7802369415 = 2*5*48096371

45. 5^4*1609*8237 - 7801426395 = 2*5*48190673

46. 5^4*1609*8237 - 7801362495 = 2*5*48197063

47. 5^4*1609*8237 - 7692381045 = 2^4*5*7386901

48. 5^4*1609*8237 - 7659428310 = 5*124780963

49. 5^4*1609*8237 - 7652941380 = 5*126078349

50. 5^4*1609*8237 - 7652843910 = 5*126097843

51. 5^4*1609*8237 - 7645931280 = 5*127480369

52. 5^4*1609*8237 - 7645928310 = 5*127480963

53. 5^4*1609*8237 - 7645283910 = 5*127609843

54. 5^4*1609*8237 - 7643528910 = 5*127960843

55. 5^4*1609*8237 - 7643158290 = 5*128034967

56. 5^4*1609*8237 - 7642958310 = 5*128074963

57. 5^4*1609*8237 - 7638512940 = 5*128964037

58. 5^4*1609*8237 - 7625941380 = 5*41*3206789

59. 5^4*1609*8237 - 7618492053 = 2^4*7*5936081

60. 5^4*1609*8237 - 7614852930 = 5*41*3260879

61. 5^4*1609*8237 - 7614502983 = 2*6803*49157

62. 5^4*1609*8237 - 7612953840 = 5*461*290837

63. 5^4*1609*8237 - 7610289354 = 157*4286903

64. 5^4*1609*8237 - 7609428315 = 2*5*67390481

65. 5^4*1609*8237 - 7604392815 = 2*5*67894031

66. 5^4*1609*8237 - 7604298315 = 2*5*67903481

67. 5^4*1609*8237 - 7602841395 = 2*5*68049173

68. 5^4*1609*8237 - 7596403128 = 13*52840769

69. 5^4*1609*8237 - 7596314280 = 5*29*4738061

70. 5^4*1609*8237 - 7596314208 = 13*52847609

71. 5^4*1609*8237 - 7594012368 = 479*503*2861

72. 5^4*1609*8237 - 7593684120 = 5*683*201947

73. 5^4*1609*8237 - 7589361240 = 5*29*4786013

74. 5^4*1609*8237 - 7584901632 = 139*5024687

75. 5^4*1609*8237 - 7583190246 = 47*53*281069

76. 5^4*1609*8237 - 7582139640 = 5*140238697

77. 5^4*1609*8237 - 7569342810 = 5*142798063

78. 5^4*1609*8237 - 7569314280 = 5*142803769

79. 5^4*1609*8237 - 7562304981 = 2^4*59*763801

80. 5^4*1609*8237 - 7548069312 = 157*4683209

81. 5^4*1609*8237 - 7546928310 = 5*147280963

82. 5^4*1609*8237 - 7542968310 = 5*148072963

83. 5^4*1609*8237 - 7542936810 = 5*148079263

84. 5^4*1609*8237 - 7542608391 = 2*587*630941

85. 5^4*1609*8237 - 7542139608 = 1823*406579

86. 5^4*1609*8237 - 7541963028 = 13*57028469

87. 5^4*1609*8237 - 7541386902 = 18257*40639

88. 5^4*1609*8237 - 7538214690 = 5*149023687

89. 5^4*1609*8237 - 7534692810 = 5*149728063

90. 5^4*1609*8237 - 7534296810 = 5*149807263

91. 5^4*1609*8237 - 7531409628 = 13*57840269

92. 5^4*1609*8237 - 7519408263 = 2*83*4601957

93. 5^4*1609*8237 - 7518034296 = 31*24687059

94. 5^4*1609*8237 - 7509463128 = 6053*127849

95. 5^4*1609*8237 - 7496513820 = 5*23*6841907

96. 5^4*1609*8237 - 7490286315 = 2*5*79304681

97. 5^4*1609*8237 - 7490268315 = 2*5*79306481

98. 5^4*1609*8237 - 7469280351 = 2*587*693401

99. 5^4*1609*8237 - 7465932810 = 5*239*684017

100. 5^4*1609*8237 - 7462938510 = 5*164078923

101. 5^4*1609*8237 - 7462153890 = 5*23*7140689

102. 5^4*1609*8237 - 7438621590 = 5*168942307

103. 5^4*1609*8237 - 7436815092 = 29*857*34061

104. 5^4*1609*8237 - 7435916820 = 5*83*2041967

105. 5^4*1609*8237 - 7432159680 = 5*170234689

106. 5^4*1609*8237 - 7421836095 = 2*5*86149703

107. 5^4*1609*8237 - 7419862035 = 2*5*86347109

108. 5^4*1609*8237 - 7419825630 = 5*2069*83471

109. 5^4*1609*8237 - 7412935860 = 5*2069*84137

110. 5^4*1609*8237 - 7409623158 = 13*67208459

111. 5^4*1609*8237 - 7409563182 = 347*2518069

112. 5^4*1609*8237 - 7409263815 = 2*5*87406931

113. 5^4*1609*8237 - 7406392815 = 2*5*87694031

114. 5^4*1609*8237 - 7406135982 = 47*569*32801

115. 5^4*1609*8237 - 7403926815 = 2*5*87940631

116. 5^4*1609*8237 - 7403851926 = 23*59*648107

117. 5^4*1609*8237 - 7392615408 = 8429*105673

118. 5^4*1609*8237 - 7391504862 = 167*5340289

119. 5^4*1609*8237 - 7369251408 = 31*29486507

120. 5^4*1609*8237 - 7368512940 = 5*182964037

121. 5^4*1609*8237 - 7365129480 = 5*183640729

122. 5^4*1609*8237 - 7362951480 = 5*184076329

123. 5^4*1609*8237 - 7362851490 = 5*184096327

124. 5^4*1609*8237 - 7362149580 = 5*184236709

125. 5^4*1609*8237 - 7362148590 = 5*184236907

126. 5^4*1609*8237 - 7361852940 = 5*184296037

127. 5^4*1609*8237 - 7361528490 = 5*184360927

128. 5^4*1609*8237 - 7358204196 = 269*857*4013

129. 5^4*1609*8237 - 7352869410 = 5*186092743

130. 5^4*1609*8237 - 7352861490 = 5*186094327

131. 5^4*1609*8237 - 7352846910 = 5*186097243

132. 5^4*1609*8237 - 7351462980 = 5*186374029

133. 5^4*1609*8237 - 7348629510 = 5*186940723

134. 5^4*1609*8237 - 7346051982 = 1607*583249

135. 5^4*1609*8237 - 7345890126 = 3461*270859

136. 5^4*1609*8237 - 7345286910 = 5*187609243

137. 5^4*1609*8237 - 7340895162 = 149*6325087

138. 5^4*1609*8237 - 7309681542 = 167*5830249

139. 5^4*1609*8237 - 7304692815 = 2*5*97864031

140. 5^4*1609*8237 - 7268059134 = 193*5260487

141. 5^4*1609*8237 - 7235910468 = 1453*720869

142. 5^4*1609*8237 - 7231598640 = 5*210346897

143. 5^4*1609*8237 - 7231485690 = 5*210369487

144. 5^4*1609*8237 - 7213945860 = 5*6287*34019

145. 5^4*1609*8237 - 7198235460 = 5*293*740681

146. 5^4*1609*8237 - 7194835206 = 29*647*58013

147. 5^4*1609*8237 - 7190645238 = 23*47508169

148. 5^4*1609*8237 - 7190354628 = 13*84075269

149. 5^4*1609*8237 - 7162089534 = 13*86249507

150. 5^4*1609*8237 - 7132495680 = 5*230167489

151. 5^4*1609*8237 - 7132459680 = 5*230174689

152. 5^4*1609*8237 - 7123904658 = 269*743*5801

153. 5^4*1609*8237 - 7096584312 = 41*359*80627

154. 5^4*1609*8237 - 7065149328 = 59*20647183

155. 5^4*1609*8237 - 7058439612 = 59*3041*6827

156. 5^4*1609*8237 - 7051942863 = 2*683*901457

157. 5^4*1609*8237 - 7039216854 = 1543*806297

158. 5^4*1609*8237 - 7032691584 = 19^2*43*80567

159. 5^4*1609*8237 - 7028951364 = 643*1950827

160. 5^4*1609*8237 - 7015429368 = 859*1476023

161. 5^4*1609*8237 - 6982415730 = 5*260183479

162. 5^4*1609*8237 - 6981345720 = 5*260397481

163. 5^4*1609*8237 - 6975301482 = 23*56870941

164. 5^4*1609*8237 - 6948135720 = 5*267039481

165. 5^4*1609*8237 - 6943825710 = 5*267901483

166. 5^4*1609*8237 - 6943815720 = 5*267903481

167. 5^4*1609*8237 - 6934815720 = 5*269703481

168. 5^4*1609*8237 - 6931485720 = 5*270369481

169. 5^4*1609*8237 - 6930258471 = 2*89*7601543

170. 5^4*1609*8237 - 6921570384 = 1697*802453

171. 5^4*1609*8237 - 6915327048 = 5683*240719

172. 5^4*1609*8237 - 6914325780 = 5*89*3076421

173. 5^4*1609*8237 - 6879512430 = 5*280764139

174. 5^4*1609*8237 - 6879352410 = 5*280796143

175. 5^4*1609*8237 - 6875293410 = 5*281607943

176. 5^4*1609*8237 - 6874352910 = 5*281796043

177. 5^4*1609*8237 - 6873529410 = 5*281960743

178. 5^4*1609*8237 - 6873512940 = 5*281964037

179. 5^4*1609*8237 - 6859307124 = 293*4860157

180. 5^4*1609*8237 - 6852379410 = 5*286190743

181. 5^4*1609*8237 - 6851293470 = 5*286407931

182. 5^4*1609*8237 - 6851279430 = 5*286410739

183. 5^4*1609*8237 - 6849153270 = 5*47*6102893

184. 5^4*1609*8237 - 6847352910 = 5*287196043

185. 5^4*1609*8237 - 6845237910 = 5*287619043

186. 5^4*1609*8237 - 6843752910 = 5*287916043

187. 5^4*1609*8237 - 6843527910 = 5*287961043

188. 5^4*1609*8237 - 6843512970 = 5*287964031

189. 5^4*1609*8237 - 6842395710 = 5*41*7028963

190. 5^4*1609*8237 - 6841973052 = 89*647*25031

191. 5^4*1609*8237 - 6837512940 = 5*289164037

192. 5^4*1609*8237 - 6835279410 = 5*289610743

193. 5^4*1609*8237 - 6831425790 = 5*290381467

194. 5^4*1609*8237 - 6814325790 = 5*293801467

195. 5^4*1609*8237 - 6813947502 = 239*6148057

196. 5^4*1609*8237 - 6794315820 = 5*297803461

197. 5^4*1609*8237 - 6790431852 = 23*64908751

198. 5^4*1609*8237 - 6780324159 = 2*983*764501

199. 5^4*1609*8237 - 6759341820 = 5*304798261

200. 5^4*1609*8237 - 6758419320 = 5*304982761

201. 5^4*1609*8237 - 6751924380 = 5*306281749

202. 5^4*1609*8237 - 6751243980 = 5*306417829

203. 5^4*1609*8237 - 6743591820 = 5*307948261

204. 5^4*1609*8237 - 6739518420 = 5*308762941

205. 5^4*1609*8237 - 6738519420 = 5*308962741

206. 5^4*1609*8237 - 6738512490 = 5*308964127

207. 5^4*1609*8237 - 6735941820 = 5*309478261

208. 5^4*1609*8237 - 6735241890 = 5*309618247

209. 5^4*1609*8237 - 6715340928 = 4801*326597

210. 5^4*1609*8237 - 6708314952 = 23*68479051

211. 5^4*1609*8237 - 6582419730 = 5*340182679

212. 5^4*1609*8237 - 6579418320 = 5*340782961

213. 5^4*1609*8237 - 6579341820 = 5*340798261

214. 5^4*1609*8237 - 6549318270 = 5*346802971

215. 5^4*1609*8237 - 6549281730 = 5*346810279

216. 5^4*1609*8237 - 6548937120 = 5*346879201

217. 5^4*1609*8237 - 6547918320 = 5*347082961

218. 5^4*1609*8237 - 6543187290 = 5*348029167

219. 5^4*1609*8237 - 6542819730 = 5*348102679

220. 5^4*1609*8237 - 6539847120 = 5*348697201

221. 5^4*1609*8237 - 6539142870 = 5*4013*86927

222. 5^4*1609*8237 - 6538194720 = 5*349027681

223. 5^4*1609*8237 - 6514723890 = 5*83*4261709

224. 5^4*1609*8237 - 6482591730 = 5*360148279

225. 5^4*1609*8237 - 6481925730 = 5*360281479

226. 5^4*1609*8237 - 6473981052 = 859*2106347

227. 5^4*1609*8237 - 6439587120 = 5*368749201

228. 5^4*1609*8237 - 6439527108 = 23*80165479

229. 5^4*1609*8237 - 6438712590 = 5*368924107

230. 5^4*1609*8237 - 6431985720 = 5*370269481

231. 5^4*1609*8237 - 6429130875 = 2*5^3*7416809

232. 5^4*1609*8237 - 6412930875 = 2*5^3*7481609

233. 5^4*1609*8237 - 6379512480 = 5*380764129

234. 5^4*1609*8237 - 6379485210 = 5*41*9287063

235. 5^4*1609*8237 - 6378512490 = 5*380964127

236. 5^4*1609*8237 - 6378451920 = 5*380976241

237. 5^4*1609*8237 - 6378102594 = 2083*914657

238. 5^4*1609*8237 - 6374512980 = 5*381764029

239. 5^4*1609*8237 - 6371549028 = 67*28534091

240. 5^4*1609*8237 - 6371485290 = 5*41*9326087

241. 5^4*1609*8237 - 6371249580 = 5*382416709

242. 5^4*1609*8237 - 6359487120 = 5*384769201

243. 5^4*1609*8237 - 6358419072 = 653*2947801

244. 5^4*1609*8237 - 6351297480 = 5*386407129

245. 5^4*1609*8237 - 6351279480 = 5*386410729

246. 5^4*1609*8237 - 6351247980 = 5*386417029

247. 5^4*1609*8237 - 6351079248 = 503*821*4679

248. 5^4*1609*8237 - 6349107852 = 23*84096751

249. 5^4*1609*8237 - 6348712590 = 5*386924107

250. 5^4*1609*8237 - 6348597120 = 5*386947201

251. 5^4*1609*8237 - 6347891250 = 5^4*29*106783

252. 5^4*1609*8237 - 6345187920 = 5*387629041

253. 5^4*1609*8237 - 6345019278 = 3407*568921

254. 5^4*1609*8237 - 6342157908 = 41*6029*7853

255. 5^4*1609*8237 - 6312805974 = 67*29410853

256. 5^4*1609*8237 - 6310759482 = 5107*386249

257. 5^4*1609*8237 - 6274839510 = 5*401698723

258. 5^4*1609*8237 - 6274513980 = 5*401763829

259. 5^4*1609*8237 - 6273849510 = 5*401896723

260. 5^4*1609*8237 - 6251897430 = 5*406287139

261. 5^4*1609*8237 - 6247518930 = 5*407162839

262. 5^4*1609*8237 - 6247513980 = 5*407163829

263. 5^4*1609*8237 - 6243851970 = 5*407896231

264. 5^4*1609*8237 - 6243518970 = 5*407962831

265. 5^4*1609*8237 - 6239847510 = 5*408697123

266. 5^4*1609*8237 - 6239517480 = 5*408763129

267. 5^4*1609*8237 - 6238751940 = 5*408916237

268. 5^4*1609*8237 - 6238451970 = 5*408976231

269. 5^4*1609*8237 - 6237518940 = 5*409162837

270. 5^4*1609*8237 - 6235189470 = 5*409628731

271. 5^4*1609*8237 - 6234897510 = 5*409687123

272. 5^4*1609*8237 - 6234518970 = 5*409762831

273. 5^4*1609*8237 - 6190485372 = 25943*80671

274. 5^4*1609*8237 - 6189075324 = 23*91054687

275. 5^4*1609*8237 - 6173852940 = 5*421896037

276. 5^4*1609*8237 - 6170845932 = 26357*80149

277. 5^4*1609*8237 - 6152938470 = 5*426078931

278. 5^4*1609*8237 - 6152897430 = 5*426087139

279. 5^4*1609*8237 - 6152478930 = 5*426170839

280. 5^4*1609*8237 - 6145789302 = 607*3521489

281. 5^4*1609*8237 - 6143852970 = 5*427896031

282. 5^4*1609*8237 - 6138529470 = 5*428960731

283. 5^4*1609*8237 - 6138527940 = 5*428961037

284. 5^4*1609*8237 - 6135289470 = 5*429608731

285. 5^4*1609*8237 - 6105789342 = 283*7694501

286. 5^4*1609*8237 - 6048291375 = 2*5^3*8940167

287. 5^4*1609*8237 - 6025973814 = 23*98146057

288. 5^4*1609*8237 - 5982641730 = 5*460138279

289. 5^4*1609*8237 - 5982341760 = 5*460198273

290. 5^4*1609*8237 - 5981436720 = 5*460379281

291. 5^4*1609*8237 - 5980136742 = 409*5631287

292. 5^4*1609*8237 - 5974318260 = 5*461802973

293. 5^4*1609*8237 - 5973412068 = 5297*436081

294. 5^4*1609*8237 - 5973246180 = 5*462017389

295. 5^4*1609*8237 - 5967324180 = 5*463201789

296. 5^4*1609*8237 - 5948236710 = 5*467019283

297. 5^4*1609*8237 - 5948136720 = 5*467039281

298. 5^4*1609*8237 - 5947138620 = 5*467238901

299. 5^4*1609*8237 - 5947021638 = 41*56983207

300. 5^4*1609*8237 - 5943871620 = 5*467892301

301. 5^4*1609*8237 - 5943867120 = 5*467893201

302. 5^4*1609*8237 - 5942381760 = 5*468190273

303. 5^4*1609*8237 - 5938467120 = 5*468973201

304. 5^4*1609*8237 - 5937106428 = 26347*89051

305. 5^4*1609*8237 - 5934826710 = 5*469701283

306. 5^4*1609*8237 - 5934281760 = 5*469810273

307. 5^4*1609*8237 - 5932416780 = 5*470183269

308. 5^4*1609*8237 - 5931486720 = 5*470369281

309. 5^4*1609*8237 - 5921743680 = 5*6029*78341

310. 5^4*1609*8237 - 5917324680 = 5*473201689

311. 5^4*1609*8237 - 5901367482 = 41*58096723

312. 5^4*1609*8237 - 5893214670 = 5*478023691

313. 5^4*1609*8237 - 5879604132 = 571*4209683

314. 5^4*1609*8237 - 5871493620 = 5*482367901

315. 5^4*1609*8237 - 5837249610 = 5*489216703

316. 5^4*1609*8237 - 5837149620 = 5*489236701

317. 5^4*1609*8237 - 5832714690 = 5*490123687

318. 5^4*1609*8237 - 5832694710 = 5*490127683

319. 5^4*1609*8237 - 5831496720 = 5*490367281

320. 5^4*1609*8237 - 5831426790 = 5*490381267

321. 5^4*1609*8237 - 5794326810 = 5*497801263

322. 5^4*1609*8237 - 5793460812 = 41*60728593

323. 5^4*1609*8237 - 5793146820 = 5*498037261

324. 5^4*1609*8237 - 5781493602 = 941*2658703

325. 5^4*1609*8237 - 5742983160 = 5*6317*80429

326. 5^4*1609*8237 - 5742193086 = 43609*58271

327. 5^4*1609*8237 - 5679430218 = 41*63509827

328. 5^4*1609*8237 - 5670498312 = 8527*306419

329. 5^4*1609*8237 - 5609184372 = 31^2*457*6089

330. 5^4*1609*8237 - 5493170826 = 41*68052739

331. 5^4*1609*8237 - 5398760142 = 35149*82067

332. 5^4*1609*8237 - 5391608742 = 41*70529863

333. 5^4*1609*8237 - 5370218946 = 8501*342679

334. 5^4*1609*8237 - 5301948762 = 4271*698053

335. 5^4*1609*8237 - 5276183940 = 5*601429837

336. 5^4*1609*8237 - 5276139480 = 5*601438729

337. 5^4*1609*8237 - 5274691380 = 5*601728349

338. 5^4*1609*8237 - 5274613980 = 5*601743829

339. 5^4*1609*8237 - 5273869410 = 5*601892743

340. 5^4*1609*8237 - 5273468910 = 5*601972843

341. 5^4*1609*8237 - 5267418390 = 5*603182947

342. 5^4*1609*8237 - 5264197380 = 5*603827149

343. 5^4*1609*8237 - 5264187390 = 5*603829147

344. 5^4*1609*8237 - 5263741890 = 5*603918247

345. 5^4*1609*8237 - 5247618930 = 5*607142839

346. 5^4*1609*8237 - 5247386910 = 5*607189243

347. 5^4*1609*8237 - 5247368910 = 5*607192843

348. 5^4*1609*8237 - 5246873910 = 5*607291843

349. 5^4*1609*8237 - 5239618470 = 5*608742931

350. 5^4*1609*8237 - 5238619470 = 5*608942731

351. 5^4*1609*8237 - 5237641890 = 5*609138247

352. 5^4*1609*8237 - 5237468910 = 5*609172843

353. 5^4*1609*8237 - 5236741890 = 5*609318247

354. 5^4*1609*8237 - 5234790618 = 3541*860927

355. 5^4*1609*8237 - 5230476918 = 419*7286053

356. 5^4*1609*8237 - 5219734680 = 5*821*746309

357. 5^4*1609*8237 - 5198607342 = 401*7692583

358. 5^4*1609*8237 - 5179642380 = 5*620738149

359. 5^4*1609*8237 - 5178936420 = 5*620879341

360. 5^4*1609*8237 - 5178642390 = 5*620938147

361. 5^4*1609*8237 - 5173862940 = 5*621894037

362. 5^4*1609*8237 - 5167843920 = 5*623097841

363. 5^4*1609*8237 - 5167839420 = 5*623098741

364. 5^4*1609*8237 - 5164278390 = 5*623810947

365. 5^4*1609*8237 - 5163978420 = 5*623870941

366. 5^4*1609*8237 - 5163948072 = 4793*650821

367. 5^4*1609*8237 - 5163742890 = 5*623918047

368. 5^4*1609*8237 - 5162873940 = 5*624091837

369. 5^4*1609*8237 - 5162839470 = 5*624098731

370. 5^4*1609*8237 - 5162378940 = 5*624190837

371. 5^4*1609*8237 - 5146783920 = 5*627309841

372. 5^4*1609*8237 - 5143867920 = 5*627893041

373. 5^4*1609*8237 - 5142976380 = 5*628071349

374. 5^4*1609*8237 - 5142796380 = 5*628107349

375. 5^4*1609*8237 - 5138796420 = 5*628907341

376. 5^4*1609*8237 - 5138679420 = 5*628930741

377. 5^4*1609*8237 - 5138629470 = 5*628940731

378. 5^4*1609*8237 - 5136742890 = 5*629318047

379. 5^4*1609*8237 - 5136427890 = 5*629381047

380. 5^4*1609*8237 - 5134628970 = 5*629740831

381. 5^4*1609*8237 - 5127890364 = 607*5198423

382. 5^4*1609*8237 - 5063984712 = 41*78520693

383. 5^4*1609*8237 - 4968750132 = 401*8265793

384. 5^4*1609*8237 - 4932175680 = 5*670231489

385. 5^4*1609*8237 - 4907281356 = 4621*730589

386. 5^4*1609*8237 - 4895213706 = 41*82637059

387. 5^4*1609*8237 - 4879621530 = 5*680742319

388. 5^4*1609*8237 - 4879362510 = 5*680794123

389. 5^4*1609*8237 - 4873621590 = 5*681942307

390. 5^4*1609*8237 - 4872593610 = 5*682147903

391. 5^4*1609*8237 - 4863579012 = 409*8361257

392. 5^4*1609*8237 - 4862713590 = 5*684123907

393. 5^4*1609*8237 - 4862379510 = 5*684190723

394. 5^4*1609*8237 - 4861723590 = 5*684321907

395. 5^4*1609*8237 - 4859637120 = 5*684739201

396. 5^4*1609*8237 - 4859372610 = 5*684792103

397. 5^4*1609*8237 - 4837629510 = 5*689140723

398. 5^4*1609*8237 - 4837261590 = 5*689214307

399. 5^4*1609*8237 - 4837162590 = 5*689234107

400. 5^4*1609*8237 - 4837126590 = 5*689241307

401. 5^4*1609*8237 - 4836297510 = 5*689407123

402. 5^4*1609*8237 - 4836271590 = 5*689412307

403. 5^4*1609*8237 - 4832695710 = 5*690127483

404. 5^4*1609*8237 - 4832591760 = 5*690148273

405. 5^4*1609*8237 - 4831695720 = 5*690327481

406. 5^4*1609*8237 - 4769152380 = 5*702836149

407. 5^4*1609*8237 - 4768513920 = 5*702963841

408. 5^4*1609*8237 - 4765183920 = 5*703629841

409. 5^4*1609*8237 - 4762518930 = 5*704162839

410. 5^4*1609*8237 - 4761523980 = 5*704361829

411. 5^4*1609*8237 - 4759236810 = 5*704819263

412. 5^4*1609*8237 - 4758692310 = 5*704928163

413. 5^4*1609*8237 - 4758691320 = 5*704928361

414. 5^4*1609*8237 - 4752613980 = 5*706143829

415. 5^4*1609*8237 - 4752386910 = 5*706189243

416. 5^4*1609*8237 - 4751926380 = 5*706281349

417. 5^4*1609*8237 - 4751623980 = 5*706341829

418. 5^4*1609*8237 - 4739861520 = 5*708694321

419. 5^4*1609*8237 - 4735980612 = 41*86520793

420. 5^4*1609*8237 - 4735926810 = 5*709481263

421. 5^4*1609*8237 - 4735268910 = 5*709612843

422. 5^4*1609*8237 - 4735168920 = 5*709632841

423. 5^4*1609*8237 - 4732159680 = 5*710234689

424. 5^4*1609*8237 - 4681359720 = 5*720394681

425. 5^4*1609*8237 - 4659237810 = 5*724819063

426. 5^4*1609*8237 - 4658791320 = 5*724908361

427. 5^4*1609*8237 - 4652873910 = 5*726091843

428. 5^4*1609*8237 - 4652791380 = 5*726108349

429. 5^4*1609*8237 - 4652783910 = 5*726109843

430. 5^4*1609*8237 - 4651783920 = 5*726309841

431. 5^4*1609*8237 - 4638527910 = 5*728961043

432. 5^4*1609*8237 - 4638517920 = 5*728963041

433. 5^4*1609*8237 - 4638259710 = 5*729014683

434. 5^4*1609*8237 - 4637528910 = 5*729160843

435. 5^4*1609*8237 - 4635917820 = 5*729483061

436. 5^4*1609*8237 - 4635178920 = 5*729630841

437. 5^4*1609*8237 - 4631970582 = 41*89057623

438. 5^4*1609*8237 - 4619325780 = 5*732801469

439. 5^4*1609*8237 - 4610937582 = 41*89570623

440. 5^4*1609*8237 - 4607395182 = 41*89657023

441. 5^4*1609*8237 - 4586319720 = 5*739402681

442. 5^4*1609*8237 - 4582139670 = 5*740238691

443. 5^4*1609*8237 - 4579136820 = 5*740839261

444. 5^4*1609*8237 - 4569317280 = 5*742803169

445. 5^4*1609*8237 - 4539867120 = 5*748693201

446. 5^4*1609*8237 - 4538269710 = 5*749012683

447. 5^4*1609*8237 - 4537916820 = 5*749083261

448. 5^4*1609*8237 - 4536819720 = 5*749302681

449. 5^4*1609*8237 - 4509368712 = 4073*926581

450. 5^4*1609*8237 - 4506893712 = 743*5082691

451. 5^4*1609*8237 - 4395126078 = 67*58032941

452. 5^4*1609*8237 - 4387615290 = 5*9467*82301

453. 5^4*1609*8237 - 4381657920 = 5*83*9401627

454. 5^4*1609*8237 - 4376512980 = 5*781364029

455. 5^4*1609*8237 - 4371298560 = 5*782406913

456. 5^4*1609*8237 - 4368527910 = 5*782961043

457. 5^4*1609*8237 - 4368512970 = 5*782964031

458. 5^4*1609*8237 - 4367851920 = 5*783096241

459. 5^4*1609*8237 - 4367512980 = 5*783164029

460. 5^4*1609*8237 - 4365127980 = 5*783641029

461. 5^4*1609*8237 - 4361852970 = 5*784296031

462. 5^4*1609*8237 - 4361798520 = 5*784306921

463. 5^4*1609*8237 - 4361527980 = 5*784361029

464. 5^4*1609*8237 - 4359871620 = 5*784692301

465. 5^4*1609*8237 - 4359867120 = 5*784693201

466. 5^4*1609*8237 - 4351867920 = 5*786293041

467. 5^4*1609*8237 - 4351627980 = 5*786341029

468. 5^4*1609*8237 - 4351267980 = 5*786413029

469. 5^4*1609*8237 - 4302167598 = 67*59420381

470. 5^4*1609*8237 - 4301952768 = 59*67481023

471. 5^4*1609*8237 - 4276958310 = 5*801274963

472. 5^4*1609*8237 - 4276503918 = 67*59803421

473. 5^4*1609*8237 - 4268751390 = 5*802916347

474. 5^4*1609*8237 - 4267519380 = 5*803162749

475. 5^4*1609*8237 - 4259736810 = 5*804719263

476. 5^4*1609*8237 - 4258697310 = 5*804927163

477. 5^4*1609*8237 - 4251736890 = 5*806319247

478. 5^4*1609*8237 - 4237596810 = 5*809147263

479. 5^4*1609*8237 - 4235976810 = 5*809471263

480. 5^4*1609*8237 - 4231865790 = 5*810293467

481. 5^4*1609*8237 - 4182359760 = 5*820194673

482. 5^4*1609*8237 - 4178659320 = 5*820934761

483. 5^4*1609*8237 - 4173658092 = 8923*460571

484. 5^4*1609*8237 - 4168259730 = 5*823014679

485. 5^4*1609*8237 - 4168235790 = 5*823019467

486. 5^4*1609*8237 - 4167958320 = 5*823074961

487. 5^4*1609*8237 - 4167935820 = 5*823079461

488. 5^4*1609*8237 - 4167529380 = 5*823160749

489. 5^4*1609*8237 - 4165237890 = 5*823619047

490. 5^4*1609*8237 - 4159678320 = 5*824730961

491. 5^4*1609*8237 - 4159367820 = 5*824793061

492. 5^4*1609*8237 - 4138265790 = 5*829013467

493. 5^4*1609*8237 - 4135960872 = 51439*80627

494. 5^4*1609*8237 - 4135267890 = 5*829613047

495. 5^4*1609*8237 - 4132695780 = 5*830127469

496. 5^4*1609*8237 - 4132685790 = 5*830129467

497. 5^4*1609*8237 - 4089573162 = 4253*986071

498. 5^4*1609*8237 - 4031296758 = 59*72068413

499. 5^4*1609*8237 - 3976284510 = 5*861409723

500. 5^4*1609*8237 - 3976214580 = 5*861423709

501. 5^4*1609*8237 - 3974628510 = 5*861740923

502. 5^4*1609*8237 - 3972845061 = 2^10*47*89563

503. 5^4*1609*8237 - 3972815640 = 5*862103497

504. 5^4*1609*8237 - 3972584610 = 5*862149703

505. 5^4*1609*8237 - 3971460258 = 509*8471263

506. 5^4*1609*8237 - 3971264580 = 5*862413709

507. 5^4*1609*8237 - 3962714580 = 5*864123709

508. 5^4*1609*8237 - 3961728540 = 5*864320917

509. 5^4*1609*8237 - 3961478520 = 5*864370921

510. 5^4*1609*8237 - 3958472610 = 5*864972103

511. 5^4*1609*8237 - 3958471620 = 5*864972301

512. 5^4*1609*8237 - 3947065218 = 58109*74623

513. 5^4*1609*8237 - 3946712580 = 5*867324109

514. 5^4*1609*8237 - 3946278510 = 5*867410923

515. 5^4*1609*8237 - 3946271580 = 5*867412309

516. 5^4*1609*8237 - 3946172580 = 5*867432109

517. 5^4*1609*8237 - 3945872610 = 5*867492103

518. 5^4*1609*8237 - 3894560712 = 56093*78241

519. 5^4*1609*8237 - 3765189420 = 5*903628741

520. 5^4*1609*8237 - 3764518920 = 5*903762841

521. 5^4*1609*8237 - 3764251890 = 5*903816247

522. 5^4*1609*8237 - 3764195820 = 5*903827461

523. 5^4*1609*8237 - 3761542890 = 5*139^2*46807

524. 5^4*1609*8237 - 3761489520 = 5*904368721

525. 5^4*1609*8237 - 3759426810 = 5*904781263

526. 5^4*1609*8237 - 3752618940 = 5*906142837

527. 5^4*1609*8237 - 3752468910 = 5*906172843

528. 5^4*1609*8237 - 3751896420 = 5*906287341

529. 5^4*1609*8237 - 3751426890 = 5*906381247

530. 5^4*1609*8237 - 3745209861 = 2^10*967*4583

531. 5^4*1609*8237 - 3745168920 = 5*907632841

532. 5^4*1609*8237 - 3742516890 = 5*908163247

533. 5^4*1609*8237 - 3741965820 = 5*908273461

534. 5^4*1609*8237 - 3681459720 = 5*920374681

535. 5^4*1609*8237 - 3679145820 = 5*920837461

536. 5^4*1609*8237 - 3659427810 = 5*924781063

537. 5^4*1609*8237 - 3652897410 = 5*926087143

538. 5^4*1609*8237 - 3651289470 = 5*926408731

539. 5^4*1609*8237 - 3645927810 = 5*927481063

540. 5^4*1609*8237 - 3645917820 = 5*927483061

541. 5^4*1609*8237 - 3645278910 = 5*927610843

542. 5^4*1609*8237 - 3645178920 = 5*927630841

543. 5^4*1609*8237 - 3642795810 = 5*928107463

544. 5^4*1609*8237 - 3641825790 = 5*928301467

545. 5^4*1609*8237 - 3641597820 = 5*928347061

546. 5^4*1609*8237 - 3615270984 = 563*8291407

547. 5^4*1609*8237 - 3582714690 = 5*940123687

548. 5^4*1609*8237 - 3582174690 = 5*940231687

549. 5^4*1609*8237 - 3579426810 = 5*940781263

550. 5^4*1609*8237 - 3578214690 = 5*941023687

551. 5^4*1609*8237 - 3574296810 = 5*941807263

552. 5^4*1609*8237 - 3569814720 = 5*942703681

553. 5^4*1609*8237 - 3569247810 = 5*942817063

554. 5^4*1609*8237 - 3568940172 = 56039*84127

555. 5^4*1609*8237 - 3568194720 = 5*943027681

556. 5^4*1609*8237 - 3548269710 = 5*947012683

557. 5^4*1609*8237 - 3547916820 = 5*947083261

558. 5^4*1609*8237 - 3526790184 = 9203*516847

559. 5^4*1609*8237 - 3519480726 = 59*80743261

560. 5^4*1609*8237 - 3482715690 = 5*960123487

561. 5^4*1609*8237 - 3481965720 = 5*960273481

562. 5^4*1609*8237 - 3465897120 = 5*963487201

563. 5^4*1609*8237 - 3452891076 = 64381*75029

564. 5^4*1609*8237 - 3061789254 = 643*8120597

565. 5^4*1609*8237 - 2976135048 = 653*8127409

566. 5^4*1609*8237 - 2840195736 = 6521*834709

567. 5^4*1609*8237 - 2793156084 = 61547*89203

568. 5^4*1609*8237 - 2793016584 = 67*81945023

569. 5^4*1609*8237 - 2671049358 = 60457*92831

570. 5^4*1609*8237 - 2638570194 = 67*84250193

571. 5^4*1609*8237 - 2481693750 = 5^4*7*1326089

572. 5^4*1609*8237 - 2463971508 = 6907*842531

573. 5^4*1609*8237 - 1987036254 = 9203*684157

574. 5^4*1609*8237 - 1965407382 = 643*9825701

575. 5^4*1609*8237 - 1937854602 = 76541*82903

With the two tables on hand I can now step through my cascades without having to redo the arithmetic over and over again. I can explore tens of thousands cascades instead of just a few hundred. I'm already finding that 48-term cascades may be the largest possible.